What are some examples of statistical AI applied to real-world problems?
There are several examples. For example, one instance of using Statistical AI from my workplace is:


Analyzing the behavior of the customer and their food-ordering trends, and then trying to upsell by recommending them the dishes which they might like to order/eat. This can be done through the apriori and FP-growth algorithms. We then, automated the algorithm, and then the algorithm improves itself through an Ordered/Not-Ordered metric.
Self-driving cars. They use reinforcement and supervised learning algorithms for learning the route and the gradient/texture of the road.